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Uspekhi Mat. Nauk, 1986, Volume 41, Issue 3(249), Pages 45–67 (Mi umn2078)  

This article is cited in 30 scientific papers (total in 31 papers)

Progress in the topology of real algebraic varieties over the last six years

O. Ya. Viro


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English version:
Russian Mathematical Surveys, 1986, 41:3, 55–82

Bibliographic databases:

UDC: 515.16
MSC: 14P25, 14Q05, 14Hxx, 14Nxx
Received: 22.05.1985

Citation: O. Ya. Viro, “Progress in the topology of real algebraic varieties over the last six years”, Uspekhi Mat. Nauk, 41:3(249) (1986), 45–67; Russian Math. Surveys, 41:3 (1986), 55–82

Citation in format AMSBIB
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\by O.~Ya.~Viro
\paper Progress in the topology of real algebraic varieties over the last six years
\jour Uspekhi Mat. Nauk
\yr 1986
\vol 41
\issue 3(249)
\pages 45--67
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\transl
\jour Russian Math. Surveys
\yr 1986
\vol 41
\issue 3
\pages 55--82
\crossref{https://doi.org/10.1070/RM1986v041n03ABEH003317}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. B. Korchagin, E. I. Shustin, “Affine curves of degree 6 and smoothings of a nondegenerate sixth order singular point”, Math. USSR-Izv., 33:3 (1989), 501–520  mathnet  crossref  mathscinet  zmath
    2. V. N. Karpushkin, “Topology of the zeros of eigenfunctions”, Funct. Anal. Appl., 23:2 (1989), 218–220  mathnet  crossref  mathscinet  zmath  isi
    3. E. I. Shustin, “New restrictions on the topology of real curves of degree a multiple of 8”, Math. USSR-Izv., 37:2 (1991), 421–443  mathnet  crossref  mathscinet  zmath  adsnasa
    4. V. N. Karpushkin, “Bounds for the Betti numbers of a level surface of a harmonic polynomial”, Funct. Anal. Appl., 26:4 (1992), 300–302  mathnet  crossref  mathscinet  zmath  isi
    5. V. A. Krasnov, “On cohomology classes defined by the real points of a real algebraic $\operatorname{GM}$-surface”, Russian Acad. Sci. Izv. Math., 43:2 (1994), 385–395  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. V. A. Krasnov, “On equivariant Grothendieck cohomology of a real algebraic variety, and its applications”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 461–477  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. A. I. Degtyarev, V. I. Zvonilov, “Rigid isotopy classification of real algebraic curves of bidegree $(3,3)$ on quadrics”, Math. Notes, 66:6 (1999), 670–674  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. V. A. Krasnov, “Real algebraic varieties without real points”, Izv. Math., 63:4 (1999), 757–790  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. S. Yu. Orevkov, “Link Theory and New Restrictions for $M$-Curves of Degree Nine”, Funct. Anal. Appl., 34:3 (2000), 229–231  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. A. I. Degtyarev, V. M. Kharlamov, “Topological properties of real algebraic varieties: du coté de chez Rokhlin”, Russian Math. Surveys, 55:4 (2000), 735–814  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. V. I. Arnol'd, “I. G. Petrovskii, Hilbert's topological problems, and modern mathematics”, Russian Math. Surveys, 57:4 (2002), 833–845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    12. B. Chevallier, “Four $M$-Curves of Degree $\boldsymbol{8}$”, Funct. Anal. Appl., 36:1 (2002), 76–78  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. Welschinger, JY, “Real algebraic curves and flexible curves on regulated surfaces of base CP1”, Proceedings of the London Mathematical Society, 85 (2002), 367  crossref  mathscinet  zmath  isi
    14. Touze, SFL, “A flexible affine M-sextic which is algebraically unrealizable”, Journal of Algebraic Geometry, 11:2 (2002), 293  mathscinet  zmath  isi
    15. Ilia Itenberg, Eugenii Shustin, “Viro theorem and topology of real and complex combinatorial hypersurfaces”, Isr J Math, 133:1 (2003), 189  crossref  mathscinet  zmath  isi  elib
    16. S. Yu. Orevkov, E. I. Shustin, “Pseudoholomorphic algebraically unrealizable curves”, Mosc. Math. J., 3:3 (2003), 1053–1083  mathnet  mathscinet  zmath
    17. E. Fortuna, P. Gianni, P. Parenti, C. Traverso, “Algorithms to compute the topology of orientable real algebraic surfaces”, Journal of Symbolic Computation, 36:3-4 (2003), 343  crossref
    18. JIBIN LI, “HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS”, Int. J. Bifurcation Chaos, 13:01 (2003), 47  crossref
    19. Itenberg, I, “Amoebas of algebraic varieties and curve enumeration (after G. Mikhalkin)”, Asterisque, 2004, no. 294, 335  mathscinet  zmath  isi
    20. E. Fortuna, P. Gianni, D. Luminati, “Algorithmical determination of the topology of a real algebraic surface”, Journal of Symbolic Computation, 38:6 (2004), 1551  crossref
    21. Florens, V, “Signatures of colored links with application to real algebraic curves”, Journal of Knot Theory and Its Ramifications, 14:7 (2005), 883  crossref  mathscinet  zmath  isi  elib
    22. O. Ya. Viro, “Whitney number of closed real algebraic affine curve of type I”, Mosc. Math. J., 6:1 (2006), 211–217  mathnet  mathscinet  zmath
    23. J. William Helton, Victor Vinnikov, “Linear matrix inequality representation of sets”, Comm Pure Appl Math, 60:5 (2007), 654  crossref  mathscinet  zmath  isi
    24. Brugalle, E, “Symmetric plane curves of degree 7: pseudoholomorphic and algebraic classifications”, Journal fur Die Reine und Angewandte Mathematik, 612 (2007), 129  crossref  mathscinet  zmath  isi  elib
    25. Gilmer, PM, “ARF invariants of real algebraic curves”, Pacific Journal of Mathematics, 230:2 (2007), 297  crossref  mathscinet  zmath  isi
    26. Erwan Brugallé, Oliver Labs, “Surfaces with many solitary points”, Geom Dedicata, 2008  crossref  mathscinet  isi
    27. Fiedler-Le Touze, S, “M-curves of degree 9 with deep nests”, Journal of the London Mathematical Society-Second Series, 79 (2009), 649  mathscinet  zmath  isi
    28. “Introduction to tropical geometry”, Tropical Algebraic Geometry, Oberwolfach Seminars, 35, 2009, 1  isi
    29. S. Finashin, V. Kharlamov, “Topology of real cubic fourfolds”, Journal of Topology, 2010  crossref  zmath  isi
    30. Alexander Nabutovsky, “Non-recursive functions, knots “with thick ropes,” and self-clenching “thick” hyperspheres”, Comm Pure Appl Math, 48:4 (2010), 381  crossref
    31. S. D'Mello, “Chord Diagrams and Generic Real Rational Planar Curves of Degree 4”, International Mathematics Research Notices, 2015  crossref
  • Успехи математических наук Russian Mathematical Surveys
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